Pattern-based quadrangulation for N-sided patches

Abstract

We propose an algorithm to quadrangulate an N-sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.

abstract = "We propose an algorithm to quadrangulate an N-sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.",

publisher = "Eurographics Association at Graz University of Technology",

number = "5",

}

TY - JOUR

T1 - Pattern-based quadrangulation for N-sided patches

AU - Takayama, Kenshi

AU - Panozzo, Daniele

AU - Sorkine-Hornung, Olga

PY - 2014

Y1 - 2014

N2 - We propose an algorithm to quadrangulate an N-sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.

AB - We propose an algorithm to quadrangulate an N-sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.